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This paper reports the first demonstration of the generation and distribution of time-bin entangled photon pairs in the 1.5-μm band using spontaneous four-wave mixing in a cooled fiber. Noise photons induced by spontaneous Raman scattering were suppressed by cooling a dispersion shifted fiber with liquid nitrogen, which resulted in a significant improvement in the visibility of two-photon interference. By using this scheme, time-bin entangled qubits were successfully distributed over 60 km of optical fiber with a visibility of 76%, which was obtained without removing accidental coincidences.
©2006 Optical Society of America
1. Introduction
The entangled states of quantum particles constitute the quintessential feature of quantum mechanics because they highlight its non-locality most vividly [1]. Moreover, entanglements form the basis of quantum information, and facilitate such applications as quantum key distribution (QKD) [2, 3], quantum teleportation [4], and quantum repeaters [5]. Of the many forms of entanglement, entangled photons are important because they are suitable for distributing quantum information over long distances. Although several good sources are available in the short wavelength band [6, 7], an entangled photon-pair source in the 1.5-μm band is needed if we are to realize quantum information systems over optical fiber networks. Recently, spontaneous four-wave mixing (SFWM) in a dispersion shifted fiber (DSF) has been drawing attention as a promising method for generating entanglement in the 1.5-μm band [8, 9, 10]. Polarization [8, 9] and time-bin entangled photons [10] have already been generated and successfully distributed over optical fibers [9, 10, 11]. In addition, quantum correlated photon pairs in the shorter wavelength bands have been generated using SFWM in photonic crystal fiber [12, 13]. The merit of this scheme is the good coupling efficiency it provides between nonlinear medium (i.e. a DSF) and transmission fibers.
Despite the series of successful experiments described above, a serious problem has been reported regarding the fiber-based photon-pair source for the 1.5-μm band, namely the existence of noise photons generated by spontaneous Raman scattering [8, 9, 10, 14, 15]. The pump light used for the SFWM process also works as the pump for the spontaneous Raman scattering process, by which Stokes and anti-Stokes photons are generated in wavelength bands longer and shorter than the pump wavelength, respectively. Consequently, accidental coincidences are caused by the Stokes and anti-Stokes photons whose wavelengths coincide with those of the idler and signal channels of photon pairs generated by SFWM. In the two-photon interference measurement, such accidental coincidences seriously degrade the visibility. As a result, the visibilities reported in the previous experiments were obtained after subtracting accidental coincidences [8, 9, 10, 11]. This large number of noise photons prevented the fiber-based photon-pair source from being applied to quantum information experiments such as QKD, because accidental coincidences result in a large bit error rate. Thus, the suppression of accidental coincidences caused by spontaneous Raman scattering is a very important issue as regards making the fiber-based photon-pair source useful in real quantum information systems.
To solve this problem, the author and K. Inoue recently demonstrated that noise photons caused by spontaneous Raman scattering were suppressed by cooling a DSF with liquid nitrogen [16]. We observed a significant enhancement of the quantum correlation characteristics in a time-correlation measurement. This report has recently been followed by a study of the generation of polarization entanglement using a cooled fiber [17]. However, it is difficult to distribute polarization qubits over optical fiber because polarization mode dispersion (PMD) induces decoherence.
In this paper, I report the first demonstration of the generation and distribution of time-bin entangled qubits using a DSF cooled by liquid nitrogen. A time-bin qubit is a superposed state spanned by two time slots [18], this means it is unaffected by PMD and thus suitable for transmission over optical fiber. With an average photon number per pulse of ~0.06, a significant improvement in the visibility from 65% to 80% was achieved by cooling the DSF, without subtracting accidental coincidences. In addition, time-bin entangled qubits were successfully distributed over 60 km (30 km × 2) of optical fiber with a visibility of 76%. This distance exceeds the previous record for the long-distance distribution of entanglement set by a group from Geneva University (25 km × 2), in which they used a lithium triborate crystal as a nonlinear medium [19].
2. Suppression of spontaneous Raman scattering by cooling fiber
Spontaneous Raman scattering is a process in which a spontaneous photon is generated by a nonlinear interaction between a pump photon and a phonon [20]. The numbers of Stokes, ns, and anti-Stokes photons, nas as a function of temperature T are expressed as [16]
where g, α, L, h, ν and kB are a gain coefficient proportional to the number of pump photons, a fiber loss coefficient, the fiber length, Planck constant, photon energy, and Boltzman constant, respectively [21]. Please note that the gain coefficient g is also related to the spontaneous Raman scattering cross section, which is dependent on phonon frequency ν. With silica-based fiber, g has its peak at ν ≃ 10 THz [22]. It is apparent that, for a fixed ν, we can reduce the number of spontaneous Raman photons by lowering the fiber temperature. If the fiber loss coefficient is independent of temperature, the ratio of the Stokes photon number at liquid nitrogen (77 K) and room temperature (293 K) with the same pump power is calculated to be ns(77)/ns(293) = 0.29. For anti-Stokes photon numbers it is nas(77)/nas(293) = 0.24. Here, I assumed that ν = 400 GHz, which corresponds to the frequency difference between the pump and signal/idler channels in the experiment. Thus, the number of noise photons is expected to be reduced by cooling the fiber with liquid nitrogen.
3. Experiments
Figure 1 shows the experimental setup. A continuous lightwave with a wavelength of 1551.1 nm from an external-cavity diode laser is modulated into double pulses with a LiNbO3 intensity modulator. The pulse width and interval are 100 ps and 1 ns, respectively. The coherence time of the continuous lightwave is ~10 μs. The double pulse is amplified by an erbium-doped fiber amplifier (EDFA), and launched into a 500-m DSF after passing through optical filters to eliminate amplified spontaneous emission noise from the EDFA. The DSF is formed into a loose coil about ~30 cm in diameter without a bobbin to reduce the bending stress, and then placed in a Styrofoam container filled with liquid nitrogen. The zero-dispersion wavelength of the DSF was 1551.1 nm. In the DSF, the double pulses work as a pump and generate time-correlated photon pairs through SFWM. The pump, signal and idler frequencies, fp, fs and fi, respectively, have the following energy conservation relationship: 2fp = fs + fi. As a result, the following time-bin entangled state is obtained at the output of the DSF [18].
Here, ∣k〉x represents a state in which there is a photon in a time slot k in a mode x, signal (s) or idler (i). ϕ is a relative phase term that is equal to 2ϕp, where ϕp is the phase difference between two pump pulses, and is stably fixed because of the long coherent time of the laser output. The output light from the DSF is input into a fiber Bragg grating (FBG) to suppress pump photons, and launched into an arrayed waveguide grating (AWG) to separate the signal and idler channels. AWG output ports with peak frequencies of +400 and -400 GHz from the pump photon frequency are used for the signal and idler, respectively. The 3-dB bandwidths of the signal and idler channels are both 25 GHz (≃0.2 nm). Then the signal and idler photons are launched into optical bandpass filters to further suppress the pump photons.
The photons output from each bandpass filter are transmitted over a 30-km DSF with a loss of 0.2 dB/km and then input into a 1-bit delayed Mach-Zehnder interferometer fabricated using planar lightwave circuit (PLC) technology [23, 10]. A state |k〉x is converted as follows by the interferometer.
Here, a and b denote two output ports of the interferometer. θx is the phase difference between the two paths of the interferometer for channel x, and can be tuned by changing the temperature. As a result, the time-bin entangled state ∣Ψ〉 is converted to
where θ = θs + θi and 16 non-coincident terms in the parentheses are not shown because they are not observed in a coincidence measurement. We can observe a two-photon interference fringe by changing θ and measuring the coincidence counts in the second time slot.
Port a of each interferometer is connected to a photon counter based on an InGaAs avalanche photodiode operated in a gated mode with a 4-MHz gate frequency. The electric signals from the photon counter for the signal and the idler are input into a time interval analyzer as a start and stop pulse, respectively. The losses of the signal and idler channels including the excess losses of the interferometers are both approximately 8 dB. The quantum efficiencies and dark count rate per gate are 8% and 4 × 10-5 for the signal, and 7% and 5 × 10-5 for the idler, respectively.
This experiment uses two detectors connected to port a of the interferometers, so only the fifth term in parentheses in Eq. (5) is observed in a two-photon interference measurement. This means that a time-bin entangled photon pair is detected with a probability of 1/8 when a constructive interference occurs (i.e. θ = ϕ). When the average number of correlated photon pairs per pulse is μc (which means that the average number per time-bin qubit is 2μc), the count rate of correlated events in a constructive interference, Rc, is expressed as
where αs and αi denote transmittances for the signal and idler channels including the quantum efficiency of the photon counters, respectively. On the other hand, the accidental coincidence rate Racc is given by
where μx and dx denote the average number of photons per pulse and the dark count rate of the detector for channel x with x = s, i, respectively. If the average number of noise photons per pulse for channel x is given by μnx, μx is expressed as
A count rate of Rc + Racc and Racc is observed at the maximum and minimum points of a two-photon interference fringe. Therefore, the visibility V is expressed as
Fig. 2. Two-photon interference fringes when the DSF was (a) at room temperature and (b) in liquid nitrogen.
First, I confirmed the effectiveness of fiber cooling for improving the visibility of two-photon interference without connecting 30-km DSF spools. I changed θi by changing the temperature of the interferometer for the idler, while fixing θs, and recorded the coincidence counts. μs and μi were set at approximately 0.05 and 0.06, respectively, for both the cooled and uncooled experiments [24]. The average count rates of the signal and idler channels, respectively, were approximately 1500 and 1600 Hz throughout measurements. Without cooling the DSF, the visibility of the two-photon interference fringe was 64.7%, which was obtained without removing the accidental coincidences (Fig. 2 (a)). Figure 2 (b) shows the fringe when the DSF was cooled. The level of the minimum points of a fringe corresponds to the number of accidental coincidences, which is proportional to μsμi as shown in Eq. (7). Because μs and μi were set at the same value for both measurements, the minimum points of both fringes were at almost the same level, as seen in Fig. 2. However, the peak level of the fringe increased significantly when the DSF was cooled. This implies that the number of noise photons is suppressed and so the portion of correlated photon pairs is effectively increased by cooling the DSF. As a result, the visibility increased to 80.0% with the accidental coincidences included. The average number of correlated photon pairs per pulse μc can be estimated from the obtained visibilities and Eqs. (6)–(9). As a result, μc was ~0.02 when the DSF was uncooled and ~0.04 when cooled. Thus, it is experimentally confirmed that fiber cooling is effective for improving the visibility of a two-photon interference fringe.
I then inserted a 30-km DSF spool between the bandpass filter and the interferometer in both the signal and idler arms, and undertook a two-photon interference experiment. The total losses of the 30-km DSF spools, including connector and splice losses, were both ~6.5 dB. Therefore, the total loss between the cooled fiber output and the photon counter input was ~14.5 dB for both signal and idler channels. The result is shown in Fig. 3. μs and μi were again set at around 0.05 and 0.06, respectively. Squares show the coincidence rate per start pulse and x symbols show the idler count rate as a function of interferometer temperature. The average count rate for the signal was ~430 Hz. The average coincidence rate at the peak of the fringe was as low as ~0.3 Hz, which resulted in a long measurement time (the measurement shown in Fig. 3 took more than three hours to complete). The visibility of the fringe was 75.8%, which was obtained without removing accidental coincidences. Thus, time-bin entangled photon pairs were successfully distributed over 60 km (30 km × 2) of fiber.
Fig. 3. Two-photon interference fringe and idler count rate after transmission over 60-km fiber. Squares: coincidence rate per start pulse, x symbols: idler count rate.
The visibility of the fringe after removing accidental coincidences was 96.8%. This result is slightly worse than >99% visibility after the elimination of the accidental coincidences reported in [10]. This slight degradation is probably caused by the larger statistical fluctuation as a result of the smaller coincidence rate.
4. Discussions
This experiment used DSF spools because long standard single-mode fibers (SMF) with 1.3-μm zero dispersion wavelength were not available. According to the following calculation, the photons generated from this source are expected to be transmitted over 60 km of SMF, thanks to the narrow bandwidth of the signal/idler photons. Let us assume that the dispersion in the cooled fiber and the optical filters is negligible and the transmittance spectra of signal and idler channels are both Gaussian. Then, the temporal shapes of the signal and idler photons are approximated as transform-limited Gaussian pulses. The half-width at the 1/e-intensity point T 0 is expressed as √ln2/(πΔf), where Δf is the full width at half maximum of the signal/idler spectrum. After transmission over an optical fiber with length z, the half width at the 1/e-intensity point of the output pulse T 1 is expressed as [22]
where β 2 denotes second derivative of the propagation constant in optical fiber. With z = 30 km, Δf = 25 GHz and β 2 = -20 ps2/km, T 1 is calculated to be ~60 ps, which is small compared with the 1-ns pulse interval. Thus, chromatic dispersion does not seem to result in serious degradation of the visibility even when two 30-km SMF spools are used. Nevertheless, it will be important to demonstrate long-distance distribution over SMF experimentally in the future.
In this experiment, the generated two-photon state was evaluated using the visibilities of two-photon interference fringes, by which we can quantify the degree of entanglement. In fact, fringe visibility was used to evaluate the results of many previous experiments. Nevertheless, the characteristics of the generated state will be better understood if we can obtain full information on the density matrix of the two-photon state. Quantum state tomography (QST) has been used to obtain information on the density matrix of an ensemble of quantum systems including polarization entangled photon pairs [25, 26]. However, QST has not yet been conducted on time-bin or energy-time [27] entanglements, possibly because of the difficulty of implementation. Thus, a detailed investigation of the generated state using QST will constitute interesting future work.
5. Conclusion
I have reported an experimental generation of time-bin entanglement using a cooled fiber. A significant improvement in the visibility was observed by cooling the DSF with liquid nitrogen. As a result, entangled photons were successfully distributed over 60-km (30 km × 2) fibers with a fair visibility of 75.8%. The results show that a 1.5-μm band entanglement source based on a cooled fiber is a promising technology for realizing advanced quantum information systems over optical fiber networks.
Acknowledgments
The author thanks K. Inoue for helpful comments and T. Honjo for help in making the measurement software. This work was supported in part by National Institute of Information and Communications Technology (NICT) of Japan.
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